There are two very reliable Wiki websites:

www.pbworks.com
or
www.wikispaces.com

Both of these are easy to use and you just need an email to sign up. Once you have signed in, you can create your wikis - easy as that!

PBWorks:
This site allows you to create private wikis with student accounts that you can create if students do not have their own email. To sign up for a free, basic educator's wiki - please follow this link:
https://plans.pbworks.com/signup/edubasic20

For any help, you can follow these links:
http://pbworks.com/content/edu+overview
http://pbworks.com/content/edu+resources

WikiSpaces:
This site allows you to create private wikis but only after you create one and promise to use it for education only.
Here is the link:
http://www.wikispaces.com/site/for/teachers

Here is a wiki for you to play with before creating your own to get to know the program:
http://sandbox.wikispaces.com/

Here is also a Powerpoint on how to use WikiSpaces:

(created by Wikispaces)